For two intervals \(I\)  and \(J\) ,
we say that \(I\)  precedes \(J\) ,
if \(I\)  is disjoint from and to the left of \(J\) .
An interval order is a partial order \(\prec \)  on a family \(I\)  of open intervals,
such that for all \(I,J\in I\) ,
\(I \prec J\)  if and only if \(I\)  precedes \(J\)  [1]}.
Here we also call \(I\)  a representation of \(\prec \) .
